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  "Title": "Geodesic Regression",
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  "Authors@R": "c(\nperson(\"Ha-Young\", \"Shin\", email = \"hayoung.shin@gmail.com\", role = c(\"aut\", \"cre\")),\nperson(\"Hee-Seok\", \"Oh\", role = \"aut\"))",
  "Description": "Provides a gradient descent algorithm to find a geodesic\nrelationship between real-valued independent variables and a\nmanifold-valued dependent variable (i.e. geodesic regression).\nAvailable manifolds are Euclidean space, the sphere, hyperbolic\nspace, and Kendall's 2-dimensional shape space. Besides the\nstandard least-squares loss, the least absolute deviations,\nHuber, and Tukey biweight loss functions can also be used to\nperform robust geodesic regression. Functions to help choose\nappropriate cutoff parameters to maintain high efficiency for\nthe Huber and Tukey biweight estimators are included, as are\nfunctions for generating random tangent vectors from the\nRiemannian normal distributions on the sphere and hyperbolic\nspace. The n-sphere is a n-dimensional manifold: we represent\nit as a sphere of radius 1 and center 0 embedded in\n(n+1)-dimensional space. Using the hyperboloid model of\nhyperbolic space, n-dimensional hyperbolic space is embedded in\n(n+1)-dimensional Minkowski space as the upper sheet of a\nhyperboloid of two sheets. Kendall's 2D shape space with K\nlandmarks is of real dimension 2K-4; preshapes are represented\nas complex K-vectors with mean 0 and magnitude 1. Details are\ndescribed in Shin, H.-Y. and Oh, H.-S. (2020)\n<arXiv:2007.04518>. Also see Fletcher, P. T. (2013)\n<doi:10.1007/s11263-012-0591-y>.",
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  "Repository": "https://hayoungshin1.r-universe.dev",
  "Date/Publication": "2021-08-28 04:19:56 UTC",
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      "title": "Geodesic distance between two points on a manifold",
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      ]
    },
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      "title": "Gradient descent for (robust) geodesic regression",
      "topics": [
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      ]
    },
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      "title": "Gradient descent for location based on M-type estimators",
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